I'll step in for supplement Ken's answer. Just one reason?
The sights.
There are many cities with incredible sights, but few so walkable as DC. The National Mall stretches about 2.5 miles and is JAM packed with history and culture. Beyond the Lincoln Memorial, Washington Monument, Korean and Vietnam Wars, White House, US Capitol, and so on, there is an unbelievable art collection. All free.
Want to see weird modern art that makes you think Smithsonian wastes their money? Go to the Hirshhorn.
The masters? NGA East.
Antique and modern portraits? Portrait Gallery.
20 foot tall sculptures? Hishhorn or NGA sculpture garden.
Beautiful masonry? Press building, Treasury, Lincoln, etc
Walk five blocks up and eat incredible ramen, then catch an NBA or NHL game.
Metro down to SW Wharf and eat crabs by the water [I think Old Bay is gross, but you'll make up your own opinion.
Want to see the Space Shuttle? Or SR-71? Drive to Dulles Air and Space [and go hit Aslin Brewing while your'e there.]
Like animals? Check out the pandas and more at the zoo.
Interested in politics? Sit in on a Supreme Court or Congressional hearing.
See random stuff, like a Haka on the steps of the Lincoln Memorial.
Like opera, musicals, or theatre? Check out Kennedy Center.
The food is pretty good here [few to none good hole-in-the-walls in DC though.]
If beer is your scene - ChurchKey and Soverign have bottle and draft lists to rock your socks.
Into malt? Jack Rose for a bananas bottle list, plus they allow cigars.
Richmond, if you are still hankering, is a two hour drive away. It's a one nighter.

Richmond is good for some nice food, BBQ, and phenomenal beer (The Veil, Triple Crossing, The Answer - whether Randallized beers are really 'beers' is a separate conversation). Other than the beer [which can be matched by NE breweries], not much separates Richmond from any other average town, in my opinion.
Between futzing around Cape Cod and Richmond, go to the Cape for sure.
DC, on the other hand, is worth the trip. for example

It wasn't too bad downtown this morning. I know some folks out in VA have lost power, which puts things in perspective.
Went into work for a bit [we are closed], a couple cigars at the lounge, then back home. Nice break to get lots of admin work done!